I think the reason you have to completely rebuild is that other than Sale, there aren't many pieces you can really build around. When the White Sox lost 90 games in 2007 some people were calling for a total rebuild but the White Sox still had some pieces that they could at least build around and plug in some gaps.

Right now they have Sale, that's about it. The pitching is okay but Peavy is old (and hurt) and I think the jury is still out on Quintana and Santiago (God only knows if Danks will ever recover).

I don't think the jury's in on Sale, Quintana, Santiago, Reed and Jones. Danks was never particularly good in the first place. He may belong in the pen - certainly a waste of his salary, but it's a sunk cost.
When you don't have to rebuild a staff, it's a lot easier.
That said, I don't want to use Peavy, Rios, etc. to acquire mediocre AAA prospects that are ML ready either.